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How do you in partial fractions?:
z-2/4*z^2+16*z+16/(z/2*z-4-z^2+4/2*z^2-8-2/z^2+2*z)
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt((625*x^4+25*10^10*x^2)/(1+25*x^2))
3/(x^3+5)-9*x^3/(x^3+5)^2
Factor polynomial:
x^4+1
x^3-1^3+3^3-x^3
y^2/2+y^23/23
-x^7+x^6/4+9*x*5/8-9*x^4/32-x^3/8+x^2/32
Least common denominator:
(a+1/a+2)/a+1
1/(1+x^2/3)
(z/x-z+x+z/z)/x/x^2-z^2
(z/x-z+x+z/z)/x/x^2-x*z^2
Factor squared:
y^4-y^2-3
x^2+x-2
y^2-4*y+3
x^2+x-3
Identical expressions
sqrt(b)-(b- one /b^ two)/(sqrt(b)- one /sqrt(b))+(one - one /b^ two)/(sqrt(b)+ one /sqrt(b))+ two /b^(three / two)
square root of (b) minus (b minus 1 divide by b squared ) divide by ( square root of (b) minus 1 divide by square root of (b)) plus (1 minus 1 divide by b squared ) divide by ( square root of (b) plus 1 divide by square root of (b)) plus 2 divide by b to the power of (3 divide by 2)
square root of (b) minus (b minus one divide by b to the power of two) divide by ( square root of (b) minus one divide by square root of (b)) plus (one minus one divide by b to the power of two) divide by ( square root of (b) plus one divide by square root of (b)) plus two divide by b to the power of (three divide by two)
√(b)-(b-1/b^2)/(√(b)-1/√(b))+(1-1/b^2)/(√(b)+1/√(b))+2/b^(3/2)
sqrt(b)-(b-1/b2)/(sqrt(b)-1/sqrt(b))+(1-1/b2)/(sqrt(b)+1/sqrt(b))+2/b(3/2)
sqrtb-b-1/b2/sqrtb-1/sqrtb+1-1/b2/sqrtb+1/sqrtb+2/b3/2
sqrt(b)-(b-1/b²)/(sqrt(b)-1/sqrt(b))+(1-1/b²)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt(b)-(b-1/b to the power of 2)/(sqrt(b)-1/sqrt(b))+(1-1/b to the power of 2)/(sqrt(b)+1/sqrt(b))+2/b to the power of (3/2)
sqrtb-b-1/b^2/sqrtb-1/sqrtb+1-1/b^2/sqrtb+1/sqrtb+2/b^3/2
sqrt(b)-(b-1 divide by b^2) divide by (sqrt(b)-1 divide by sqrt(b))+(1-1 divide by b^2) divide by (sqrt(b)+1 divide by sqrt(b))+2 divide by b^(3 divide by 2)
Similar expressions
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1+1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))-(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))-2/b^(3/2)
sqrt(b)-(b+1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt(b)+(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt(b)-(b-1/b^2)/(sqrt(b)+1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)
sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)-1/sqrt(b))+2/b^(3/2)

Expression simplification/ Fraction Decomposition into the simple/ sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2)

How do you sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2) in partial fractions?

The solution

You have entered [src]

                1               1           
            b - --          1 - --          
                 2               2          
  ___           b               b        2  
\/ b  - ------------- + ------------- + ----
          ___     1       ___     1      3/2
        \/ b  - -----   \/ b  + -----   b   
                  ___             ___       
                \/ b            \/ b

$$\left(\frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} + \left(\sqrt{b} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}}\right)\right) + \frac{2}{b^{\frac{3}{2}}}$$

sqrt(b) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b)) + (1 - 1/b^2)/(sqrt(b) + 1/(sqrt(b))) + 2/b^(3/2)

General simplification [src]

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Fraction decomposition [src]

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Rational denominator [src]

         0          
--------------------
 11                 
b  *(1 + b)*(-1 + b)

$$\frac{0}{b^{11} \left(b - 1\right) \left(b + 1\right)}$$

0/(b^11*(1 + b)*(-1 + b))

Assemble expression [src]

                       1               1    
                   1 - --          b - --   
                        2               2   
  ___    2             b               b    
\/ b  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b

$$\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}}$$

sqrt(b) + 2/b^(3/2) + (1 - 1/b^2)/(sqrt(b) + 1/sqrt(b)) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b))

Trigonometric part [src]

                       1               1    
                   1 - --          b - --   
                        2               2   
  ___    2             b               b    
\/ b  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b

$$\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}}$$

sqrt(b) + 2/b^(3/2) + (1 - 1/b^2)/(sqrt(b) + 1/sqrt(b)) - (b - 1/b^2)/(sqrt(b) - 1/sqrt(b))

Combining rational expressions [src]

        /     3    2         \            /      2\                     
(1 + b)*\1 - b  + b *(-1 + b)/ + (-1 + b)*\-1 + b / + 2*(1 + b)*(-1 + b)
------------------------------------------------------------------------
                          3/2                                           
                         b   *(1 + b)*(-1 + b)

$$\frac{2 \left(b - 1\right) \left(b + 1\right) + \left(b - 1\right) \left(b^{2} - 1\right) + \left(b + 1\right) \left(- b^{3} + b^{2} \left(b - 1\right) + 1\right)}{b^{\frac{3}{2}} \left(b - 1\right) \left(b + 1\right)}$$

((1 + b)*(1 - b^3 + b^2*(-1 + b)) + (-1 + b)*(-1 + b^2) + 2*(1 + b)*(-1 + b))/(b^(3/2)*(1 + b)*(-1 + b))

Numerical answer [src]

b^0.5 + 2.0*b^(-1.5) + (1.0 - 1/b^2)/(b^0.5 + b^(-0.5)) - (b - 1/b^2)/(b^0.5 - b^(-0.5))

b^0.5 + 2.0*b^(-1.5) + (1.0 - 1/b^2)/(b^0.5 + b^(-0.5)) - (b - 1/b^2)/(b^0.5 - b^(-0.5))

Common denominator [src]

$$0$$

Powers [src]

                       1               1    
                   1 - --          b - --   
                        2               2   
  ___    2             b               b    
\/ b  + ---- + ------------- - -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b

$$\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} - \frac{b - \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}}$$

                       1           1        
                   1 - --          -- - b   
                        2           2       
  ___    2             b           b        
\/ b  + ---- + ------------- + -------------
         3/2     ___     1       ___     1  
        b      \/ b  + -----   \/ b  - -----
                         ___             ___
                       \/ b            \/ b

$$\sqrt{b} + \frac{1 - \frac{1}{b^{2}}}{\sqrt{b} + \frac{1}{\sqrt{b}}} + \frac{- b + \frac{1}{b^{2}}}{\sqrt{b} - \frac{1}{\sqrt{b}}} + \frac{2}{b^{\frac{3}{2}}}$$

sqrt(b) + 2/b^(3/2) + (1 - 1/b^2)/(sqrt(b) + 1/sqrt(b)) + (b^(-2) - b)/(sqrt(b) - 1/sqrt(b))

Combinatorics [src]

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Identical expressions

Similar expressions

How do you sqrt(b)-(b-1/b^2)/(sqrt(b)-1/sqrt(b))+(1-1/b^2)/(sqrt(b)+1/sqrt(b))+2/b^(3/2) in partial fractions?

The solution